Uniform Regularity Close to Cross Singularities in an Unstable Free Boundary Problem
نویسندگان
چکیده
منابع مشابه
Uniform Regularity Close to Cross Singularities in an Unstable Free Boundary Problem
We introduce a new method for the analysis of singularities in the unstable problem ∆u = −χ{u>0}, which arises in solid combustion as well as in the composite membrane problem. Our study is confined to points of “supercharacteristic” growth of the solution, i.e. points at which the solution grows faster than the characteristic/invariant scaling of the equation would suggest. At such points the ...
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We prove a regularity result for the unstable elliptic free boundary problem ∆u = −χ{u>0} (0.1) related to traveling waves in a problem arising in solid combustion. The maximal solution and every local minimizer of the energy are regular, that is, {u = 0} is locally an analytic surface and u|{u>0}, u|{u<0} are locally analytic functions. Moreover we prove a partial regularity result for solutio...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2010
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-010-1015-x